When you are on the booking page it will state the following;
If you are a Kew Member, please select the 'Kew Member tickets' option under your preferred entrance. Select your date/time and there will be box to enter your membership number.
Kew members can find their unique membership number on a membership card or any email correspondence with us. It will start with M or W. Email firstname.lastname@example.org if you have lost your details. Members may purchase up to 14 tickets per household.
If you have any issues with your membership, please read here.